Sur la cohomologie à support des fibrés en droites sur les variétés symétriques complètes

Tchoudjem, Alexis

doi:10.1007/s00031-010-9105-6

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Relations With Cohomology On Geometric Quotients1

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2019

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Article2

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Cited by 2 publications

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“…Remark. PGL 3 PSO 3 is not a wonderful variety of minimal rank, but Tchoudjem has shown in [24] that the cohomology groups H i (Y, L) have a similar description.…”

Section: Relations With Cohomology On Geometric Quotientsmentioning

confidence: 99%

On differential operators on complete symmetric varieties of type A1 and A2

Dejoncheere

2019

Journal of Algebra

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In this paper, we will look at the algebra of global differential operators D X on wonderful compactifications X of symmetric spaces G H of type A 1 and A 2 . We will first construct a global differential operator on these varieties that does not come from the infinitesimal action of g. We will then focus on type A 2 , where we will show that D X is an algebra of finite type, and that for any invertible sheaf L on X, H 0 (X, L) is either 0 or a simple left D X,L -module. Finally, we will show with the help of local cohomology that this is still true for higher cohomology groups H i (X, L).

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“…Remark. PGL 3 PSO 3 is not a wonderful variety of minimal rank, but Tchoudjem has shown in [24] that the cohomology groups H i (Y, L) have a similar description.…”

Section: Relations With Cohomology On Geometric Quotientsmentioning

confidence: 99%